03 · IRB — the model, constrained

Art 142–191 CRR

Purpose & history

One factor, 99.9%, and everything that follows

The IRB formula is a single economic idea: portfolio losses driven by one systematic factor (the economy), with each obligor's sensitivity set by an asset correlation R. Conditional on a 99.9th-percentile bad year, the formula asks what default rate the portfolio suffers and charges capital for the unexpected part — expected loss belongs to provisioning, and the shortfall between EL and accounting provisions is deducted from CET1. Everything else on the panel is parameterisation of that idea: R falling with PD for corporates (bigger firms fail together, small ones idiosyncratically), fixed at 0.15 for mortgages (one housing market), 0.04 for QRRE; the maturity adjustment charging migration risk on longer paper; the 0.9997-style conservatism debates that never end.

The finalisation did not reject the model — it rejected estimating it where data cannot: entities with two defaults per generation (banks, mega-corporates) lost A-IRB; every surviving input gained a floor; and the 1.06 scalar — a 2004-era calibration patch — was finally deleted. What remains is the bargain Basel II should have offered: models where defaults are countable, discipline everywhere.

Requirements

Approval lifecycleApplication per rating system and exposure class; three years' prior use experience; supervisory model investigation before permission; material changes pre-approved via the model-change RTS.

Estimation standardsPD: long-run default-weighted averages, ≥ 5y retail / 7y corporate data; LGD: economic loss incl. costs, downturn add-on, ≥ 7y; margin of conservatism per identified deficiency (EBA GL taxonomy: A/B/C categories).

Rating-system operation≥ 7 non-default grades, annual re-rating, override monitoring, human-in-the-loop governance for statistical models.

Validation & monitoringIndependent annual validation: discrimination (AUC drift), calibration (predicted vs realised), stability (PSI); backtesting registers with supervisor visibility.

Use testRatings demonstrably inside approval, pricing, limits, provisioning and management reporting — supervisors interview line staff, not just model owners.

Downturn & floorsDownturn LGD per the RTS methodology; input floors applied post-estimation (PD 5bp, LGD 25% unsecured corporate, etc.) — floors are constraints on outputs, not substitutes for estimation.

Calculations

F-IRB corporate — the full formula, once

€10m senior unsecured, PD 0.5%, F-IRB LGD 40%, M 2.5y R = 0.12·(1−e^(−50·PD))/(1−e^(−50)) + 0.24·(1−(1−e^(−50·PD))/(1−e^(−50))) = 0.2135
b = (0.11852 − 0.05478·ln PD)² = 0.1671
K = LGD·[N((G(PD) + √R·G(0.999))/√(1−R)) − PD] × (1+(M−2.5)·b)/(1−1.5·b)
= 0.40·[N(−1.294) − 0.005] × 1.334 = 0.40 × 0.0928 × 1.334 = 0.0495
RW = 12.5 × K ≈ 62% → RWA €6.19m (SA: €10m) · EL = PD×LGD = 0.20% → €20k vs provisions → shortfall to CET1 if under.

G(·) inverse standard normal · N(·) standard normal CDF · R asset correlation · b maturity adjustment · K capital per unit of EAD · under A-IRB the same machine runs with own LGD/EAD (where still permitted), floored.

Where the floors bite Prime mortgage estimated PD 3bp, LGD 4% → floored to PD 5bp, LGD 5%: RW rises ≈ 40% relative — the floors bind exactly on the portfolios the output floor also targets. Double discipline, one direction.

Scope after CRR3 — what runs on what Large corporate (rev > €500m): F-IRB or SA only · bank counterparty: F-IRB/SA · equity: SA only · retail: A-IRB only (no F-IRB exists) · sovereigns: exempt from floors. The model map is now an eligibility question before it is a modelling one.

Changes & sources

Change	Effect
A-IRB withdrawn (large corp., institutions)	Own-LGD advantage gone where defaults are unobservable
Equity → SA	All internal equity models retired
Input floors	PD 5bp (10bp QRRE revolvers), LGD/EAD floors per class
1.06 scalar deleted	−5.7% RWA on all IRB books, mechanically
F-IRB senior unsecured LGD 45→40%	Partial offset to the constraints
Partial use liberalised	Permanent SA carve-outs by class without losing IRB elsewhere

Sources: Art 142–191; EBA IRB-repair GL suite (PD/LGD estimation, downturn, MoC); model-change RTS; TRIM decisions bank-by-bank.
Watch: EBA monitoring of post-floor IRB incentives — early evidence some banks hand back approvals where the floor makes them pointless.

Independent analysis by Elderlake Partners, as at August 2026. Not legal, accounting or supervisory advice.